How can we compute the curvature/shape

[Pejeu]

of a surface of a part that rotates about a pivot point such that there is rolling instead of sliding contact at the interface between that part, along that curved surface, and another part, with a flat surface against which the first one pushes as it rotates about its pivot.

I want to design a roller rocker/finger follower engagement area with the stem of poppet valve.

How can one compute that or where can one read on how to do it?

 

[Baluncore]

I presume it is the contact between the top of the poppet valve stem and the rocker that you want to roll rather than slide.

If there is a profile that rolls, then the rocker will need a curve like a gear tooth involute, and the top of the valve stem will need to be cut with the same contact angle. That contact angle will prevent valve rotation unless some rotating cap is made to fit on top of the valve stem. That contact angle will also put a side thrust on the stem.

The way the rocker slides on the top of the stem is sometimes used to aid rotation. That will be lost with a cap.

 

[Pejeu]

Yes, that's exactly what I want. I want the end of the rocker to roll over the tip of the poppet valve stem instead of sliding against it as it pushes it down.

I was fairly sure the required profile is an involute or evolute but I don't have a clear picture of what to do.

However I don't want a rounded valve stem end. I want the valve stem to be flat. And I think it can be, that it doesn't need to be curve as well.

With gear teeth both the contact surfaces are rotating about pivot points. In this application only one contact surface is rotating.

I'm not sure what you mean by side thrust. There wouldn't be any with a flat end to the stem.

Off centre contact? That is a given and pretty much unavoidable unless a bucket tappet is used to have that grind against the bore machined in the cylinder head so that takes the cocking thrusts against the head.

 

[Baluncore]

The best model I have for the situation is a spur gear rolling along a rack.
The centre of the spur gear is your rocker shaft and the top of the valve stem is one rack tooth.
A rack is cut with a tooth face at the contact angle of the gear system. That should be between 10 and 20 degrees. But then you specify the top of the stem must be cut square, which unfortunately precludes rolling contact since the stem end is no longer the equivalent of a rack tooth face.

 

[Pejeu]

Yet there should be a solution. Isn't this how they do it in the automotive industry?

I find it hard to believe they simply allow sliding contact between the rocker and stem.

Of course, the cop-out (for me, at least) would be to use a roller at the end of the rocker arm.

However, that would run the risk of the roller running off the surface of the valve stem if the rocker swing angle is to wide or rocker is too short. It seems this approach is popular with performance OHV engines, however.

http://images.fordcobraengines.com/wp-content/uploads/2012/10/roller2.jpg

But this would require using a cap over the valve stem to increase the contact area.

Is that really how they do it? They allow sliding contact between the valve stem and rocker or simply use a roller on the tip of the latter?

 

[SteamKing]

When gas was cheap, indeed rocker arms used sliding contact between the rocker and the valve stem like this:

The push rod fits into the ball-shaped dome at the upper right. This type of rocker is very cheap to make because it is a one piece steel stamping which fits onto a steel stud support with a simple adjustment nut to keep it in place. Down below, in the engine, the valve lifter would also slide on the cam lobe. Granted that all of the surfaces are lubricated when the engine is operating, but the friction losses are quite high, especially at high RPM.

To reduce friction losses in the motor, manufacturers started to substitute roller cams and roller lifters in the late 1980's. Competition engine builders also used roller rockers like this:

This part is more expensive, but the roller reduces the friction from the sliding of the valve stem on the rocker end.

 

[Pejeu]

Many modern inline 4 cylinder engines (especially diesel engines on European makes) employ roller rockers.

But these only have a roller in the middle to avoid sliding contact with the camshaft. They slide on the tip of the hydraulic lash adjuster (which has a hemispherical tip) at one end and slide (or roll?) on the end of the valve stem at the other.

But still, do they slide or roll on the stem?

If they roll how can I plot or graph that curve so I can design my own valvetrain prototypes?