Design  of a Mechanical Shaker Table

Problem Statement

Design of electronics packaging for rugged-environment applications requires talented mechanical engineers. Vibration can bend printed circuit boards, cyclically loading the solder joints. The inertial loads of the chips can also cause solder joint fatigue. Shaker tables are used to impart a certain “g-load” to circuit boards to simulate in-service loads. 

Here’s a video showing what vibration can do to electronics. Imagine each integrated circuit pin as a flexing cantilever that bends its solder joint. 

https://www.youtube.com/watch?v=vb2QZQ9Z0vA 

A new topological design for a mechanical shaker is proposed, and your job is to investigate its technical feasibility. A steel plate is bolted to two column supports as shown below (Figure 1). A hole at midspan allows the beam to be bolted to a 2 kg assembly consisting of a rotating unbalance moe, the board to be tested, and a hollow section through which the bolt goes. The rotating unbalance creates a sinusoidal force that makes the beam flex, shaking the test specimen. The shaker must be capable of providing 50 g’s of acceleration. This must be accomplished with an unbalance rotation frequency of 200 Hz or less. Your unbalance cannot be more than 0.05 kg-m. 

Don’t worry about the details of the box, or the attachment of the box to the hollow section – just worry about the hole and bolt size where the hollow section bolts to the plate. Treat the box/hollow section as a 2 kg point mass in the middle of a flexible beam (Figure 2). Assume that the bolt grip at the attachment point is 2 x the plate thickness (l = 2t). The plate must have infinite life with a safety factor of 1.5. The bolts must also have infinite fatigue life with a safety factor of at least 1.5. Assume a small material damping ratio (a few percent). 

You are responsible for specification of:  

• plate width w, thickness t, column width b, hole separation s, span length L  

• material (specify a steel and report its strength)  

• hole diameters, bolt threads, bolt grades, and bolt lengths (centre hole and bolt can be different diameter than the four end holes/bolts) 

•  rotating unbalance magnitude and required rotational speed 

Use a computational tool such as a spreadsheet or MathCAD to flesh out a feasible first design, and then iterate to reduce the plate size, bolt size, required unbalance, etc. Write out the calculations justifying your final design on three-column design paper and submit that. 

An attempt at designing the shaker table