Motion designers choreograph the movements of parts in machines. As you'd expect, the parts in the machine always react to the planned motion. The response nominally has two components: the steady state and the transient. Often the transient is obvious as a 'residual vibration' after an index, for example. However,, all mechanisms vibrate during and after a motion, even when not observable. The level of vibration mostly determines the machine's MTBS, throughput, lifespan, maintenance schedule, life cycle cost, for example.
The machine's response to a motion depends upon the motion design . If the motion response is poor, efforts are commonly made to reconfigure the machine parts rather than redesign the motion. Redesigning parts is sometimes costly and may put project schedules back. With servos, redesigning the motion is cost free and can be carried out instantly.
Let's picture your machine part is your head, blind-folded and in a helmet! Your head is being interviewed for an astronaut's job. You are in a chair, without a head-rest, in a centrifuge, spinning at with a steady speed. Your head is being forced outwards with a constant acceleration. You will know your neck muscles must strain hard to keep your head upright at a continual position relative to your shoulders.
Now imagine a machine component. It is bolted to the chair and cantilevered over the top of the chair's back-rest; it deflects to a consistent position. Nonetheless, as long as the machine part is sufficiently strong enough to 'take the strain ', it will typically be strong enough forever.
Packaging machines have parts that move forwards and backwards, mixed together with stationary periods. Therefore, machine parts are subject to varying acceleration, not continual acceleration. Random acceleration means we must look at Jerk. Jerk is the rate of change of acceleration.
Let's imagine the centrifuge is speeding up. Think of only the increase in radial acceleration, and ignore the tangential acceleration. The muscles in your neck are in the procedure of 'exerting themselves more' to keep your head in one position. They're experiencing 'Jerk'. The muscles in your neck 'feel ' the rate of change of acceleration because they will be able to 'feel ' how swiftly the muscles must stiffen.
A mechanical element will constantly change its deflection proportionally to the acceleration it is subject to. Won't it? Yes! And No! Yes: if the jerk is 'low'. No: if the jerk is 'high'.
What's 'low' and 'high'? Let's imagine the acceleration changes from 'Level 1' to a 'Level Two'. Level Two could be larger or less than Level 1. If the acceleration is changed from Level One to Two at a 'low rate', the deflection of the element will 'more or less' be proportionate to the immediate acceleration. If it is a 'high rate', the deflection of the part will first 'lag', then 'catch up' and, if there's little damping, 'overshoot' and then repeat. This is both during and after the acceleration transition from Level 1 to Two. Complicated?
It is easier to consider the fastest conceivable rate of change of acceleration - infinite jerk. This is a step-change in applied acceleration. It can be any step size, but jerk is always infinite.
Nothing with inertia can respond to an acceleration that is meant to change in zero time. The deflection of all mechanical elements will first lag and then overshoot. They WILL vibrate. How much?
Try this experiment. Take a steel ruler - one that can simply flex, but not that much. Clamp it, or hold it to one side of a table so it overhangs . Suspend a mass above the end of the ruler from zero height - so that the mass is just kissing the ruler. Let go of the mass. You may observe the ruler deflects and vibrates. It'll deflect up to two times the deflection of the 'steady-state ' deflection. The ruler wasn't hit, because the mass was initially touching the ruler. The ruler was only subject to a step change in force - equivalent to a step-change in acceleration. A similar thing will occur if you remove the mass off the ruler. Nonetheless as the total mass is now less, it will vibrate less.
Certainly, no one would try to apply a step-change in acceleration to a mechanical system if they knew it would vibrate? Well, you would be surprised.
Getting back to your neck; playground rides control jerk really closely. Otherwise the designers would be responding to lawsuits not to the motion.
Hence a bit about Jerk - the significant motion design parameter that massively influences vibration of machine parts. The motion design software built in to MechDesigner lets you edit Jerk values to any particular value you want.
About the Author:
Doctor Kevin J Stamp is a Director of PSMotion Limited, who specialise in machine design software. PSMotion have developed MechDesigner to help design, scritinize and optimize multi-axis machines with complex motions. Kevin is a Professional Engineer with a PhD in High Speed Packaging Machine Design and 20 years experience in improveing the performance of packaging machinery. PSMotion L.T.D is based near Liverpool in the United Kingdom and was launched in 2004.
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