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The figure below shows a schematic of an automotive valve train. The rotating cam moves the pushrod ( follower ) , and the rocker -
The figure below shows a schematic of an automotive valve train. The rotating cam moves the pushrod follower and the rockerarm rotates to move the valve in the vertical direction. A simplified mechanical model is shown adjacent to the valve train schematic diagram. Moment of inertia represents the rockerarm inertia about the pivot point. Deflection of the pushrod is modeled by spring and the return spring on the valve is Friction in the rockerarm pivot is modeled by viscous coefficient The vertical motion of the cam follower is the input to the system. Angular position of the rockerarm is which is positive in the clockwise direction. When the rockerarm angle is level the return spring has a compressive preload force of When cam follower position and then the pushrod is undeflected. Assume that rockerarm angle remains small at all times.
a Draw free body diagrams for the system in terms of the given parameters and coordinates. Make sure to include displacements and label all forces and torques. Use the positive directions indicated in the schematic.
b Write the elemental equations for each of the free body diagrams in part a
c Derive the mathematical model of the valve train system and determine the required displacement of the cam follower when the system is at rest equilibrium with a level rocker
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