In December of 2019, I gave an educational seminar to a standing room only crowd at the Performance Racing Industry Tradeshow. I was asked to speak on the topic of valvetrain performance specific to offshore powerboats, and this was likely the first time this topic had been discussed publicly ever! The Camfather himself, Ed Iskenderian was among those in attendance, among many engine professionals. To say the least, I was honored. The following is part 3 of a synopsis of my talk.
Stiffnesses
In the last segment, we learned how to move masses from the cam side to the valve side, and also how to express rocker arm moment of inertia as a valve side mass. Now we’re going to start talking about the numerator of the frequency equation: stiffness.
Stiffness is a measure of how rigid something is when a load is applied to it. Since nothing in this world is perfectly rigid, everything has a stiffness associated with it. In the case of an engine valvetrain, each component has a stiffness, or spring rate. It is the sum of these spring rates that gives us the overall stiffness of a valvetrain system.
Cam Side Stiffnesses
Once we understand the nature of stiffness, in order to calculate the overall system stiffness we have to manage how that stiffness is affected by the rocker arm. In the case of mass, it was a simple division by the rocker ratio. In the case of stiffness, it’s a bit more complicated than that.
Let’s take the lifter for example. To arrive at an equivalent lifter stiffness on the valve side, we would divide the lifter’s true stiffness by the square of the rocker ratio.
This has the effect of making the cam-side stiffnesses much more important than the cam side masses, as their stiffness is so markedly reduced by the rocker ratio. From this, two key learnings can be found:
- Given a choice, minimize your rocker ratio. Put the motion into the grind of the cam
- If that can’t be done, stiffen your valvetrain on the cam side.
Now you might be thinking, “What about those NASCAR engines of years past? I heard they were running 2.20:1, 2.40:1, even 2.50:1 ratios!” You’d be right, they were (prior to when roller lifters were permitted in the Cup series, anyway), but not because that was their first choice. You see, NASCAR placed a limit on the diameter if the lifter at .875”, which placed a mechanical constraint on the velocity that could be ground into the cam. The high rocker ratios were making up for the lack of tappet velocity. It took some very stiff cam side components to make up for that high ratio. ½” pushrods were the norm (with a taper to clear the intake ports).
Pushrod Stiffness
Pushrods, the other major cam side component, are deceptively complex. While looking like a simple shaft with two balls on either end, they present a significant source of compliance (the opposite of stiffness) to the valvetrain.
First, pushrods cannot be treated as ideal columns (per classical Eulerian analysis) for three reasons:
- Pushrods always have some degree of static runout
- In addition to the linear motion, the rocker arm induces an oscillating component to the pushrod that contributes to deflection
- The rocker arm applies a bending moment to the pushrod through the ball socket joint
This deflection can be in excess of 0.050” in a racing engine, a value we most certainly want to minimize. How can we do that? Some classical mechanics of materials offers us some guidance:
Through studying the equation above, it becomes clear that a short, large OD pushrod will perform best. This is of course already well-understood by engine enthusiasts and professionals. Unfortunately, the question of pushrod length is answered during the initial engine design process. As most of us are refining an existing design rather than starting with a clean sheet of paper, length is mostly out of the question (aside from using lifters that have the pushrod socket higher in the body. Moving it too much higher will increase side loading on the lifter body, which might require some thorough durability testing to validate. Tread lightly here). Most of us will benefit most with some large (7/16”+ pushrods). Consider using some tapered pushrods that increase the diameter in the lifter valley where space constraints are more relaxed, then tapering to something that will clear the intake ports. Those airflow guys are always getting in the way of our valvetrains!
Once a stiffness value for the pushrod is determined, resolve the stiffness over to the intake valve side the same way we did the lifter above.
Rocker Arm Stiffness
Rocker arms are most likely the lowest stiffness component of your engine, so they deserve priority in your consideration when you’re addressing stiffness. Unfortunately, determining stiffness of a rocker arm requires some tools not usually found in your typical garage.
The first way is through a compression testing machine. A popular one is made by Instron. In the video at this link, the machine is demonstrated rather humorously on a paper cup. The output is a plot of force vs. displacement. The slope of this curve is the stiffness we’re looking for. This is likely the best method.
A second alternative is to create a CAD model of the part in question and perform a Finite Element Analysis on that model (FEA).
Both of these methods are outside the scope of most engine builders, and certainly most do-it-yourself engine guys. If you want help contact Allmond Marine.
In these compression testers, it’s common to constrain the pushrod socket and valve pallet or roller while loading the trunnion. Once you have that stiffness, you can express it as valve side stiffness by dividing that quantity by the quantity 1+the rocker ratio, squared.
Don’t forget that the bearing in the rocker and the stud or stand the bearing is mounted to are also not infinitely stiff. Express these as valve side stiffnesses in a similar way as you did the rocker arm.
These will make the rocker body “look” less stiff to the rest of the valvetrain.
From here, the stiffnesses on the valve side are straightforward. In the next and final segment, we will go through how to put the entire package together and arrive at the frequency of your valvetrain, then how to hit your frequency target.
