Chrysler Holding LLC

Proposed Project for the MSU Industrial Math Students

Development of an Efficiency Maximizing Tool for Custom Design of a Rocker Arm Joint

The valve train design within an engine defines the way an engine breathes. A typical pushrod or overhead cam engine has a rocker arm that helps transfer motion created by a cam follower rolling along a cam lobe, to the actual valve that opens and closes as the engine operates. The rocker arm joint, i.e., the contact joint where the valve tip touches the rocker arm, must be carefully engineered to prevent valve train noise, and to minimize wear. Wear is largely a function of sliding velocity within the joint. (Sliding velocity occurs when two surface rub against one another.) It turns out that sliding velocity is completely determined by the contact point path (the path that the contact point takes as the valve moves up and down) in space, and by the angle that the (flat) valve stem surface makes with the rocker arm. (See attached figure.) I can provide the required formulas to students. The proposal is that the student (or students) take the theory, and turn it into an applied tool. That is, write Matlab software that will allow a user to specify a contact point path in a plane, and a single angle. From these two inputs, construct the rocker arm surface that, when pushing a valve stem open and closed in pace, will generate that prescribed contact point path.

The benefit of generating such a tool is that it will enable a valve train engineer to custom design a rocker arm joint that reduces sliding velocity when wear will be highest (typically when the force between valve stem and rocker arm is high), and allow greater sliding velocity when wear will be lowest (typically when the force between valve stem and rocker arm is lower). This will potentially allow us to have greater control over the wear and friction losses within the rocker arm joint.

For any additional questions regarding the program curriculum and/or the extension deadline for the application to the MSIM program, contact us at msim@math.msu.edu

## Contact

Department of Mathematics
Michigan State University