Motion designers plan 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 2 components: the steady state and the transient. Usually the transient is obvious as a 'residual vibration' after an index, as an example. However,, all mechanisms vibrate during and after a motion, even if not observable. The scale of vibration mostly determines the machine's MTBS, capacity, life, maintenance schedule, life cycle cost, and so on.
The machine's response to a motion depends upon the motion provided for it. If the motion response is bad, efforts are often made to redesign the machine parts instead of redesign the motion. Redesigning parts is sometimes costly and will put project schedules back. With servos, redesigning the motion is free and can be carried out instantly.
Let's imagine the machine part is your head, blind-folded, 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 flung outwards with a constant acceleration. You will know must strain hard to keep your head upright at a continual position relative to your shoulders.
Now envisage a machine part. It is bolted to the chair and cantilevered over the top of the chair's back-rest; it deflects to a consistent position. Nevertheless, as long as the machine component is sufficiently strong enough to 'take the strain ', it'll usually be strong enough forever.
Packaging machines have parts that can move backwards and forwards, mixed together with dwell periods. Thus, machine parts are subject to random acceleration, not constant acceleration. Varying acceleration means we've got to look at Jerk. Jerk is therate-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 place. They're feeling 'Jerk'. Your neck muscles 'feel ' the rate of change of acceleration as they are able to 'feel ' how quickly the muscles must stiffen.
A mechanical element will continually 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 One' to a 'Level Two'. Level Two could be larger or less than Level One. 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's a 'high rate', the deflection of the component will first 'lag', then 'catch up' and, if there's little damping, 'overshoot' and then repeat. This is during and after the acceleration transition from Level One to Two. Complicated?
It is easier to consider the speediest imaginable rate of change of acceleration - infinite jerk. This is a step-change in applied acceleration. It can be any step size, but jerk is definitely infinite.
Nothing with mass can make a response to an acceleration that is intended to change in zero time. The deflection of all elements will first lag and then overshoot. They WILL vibrate. By how much?
Try this experiment. Take a steel ruler - one that can easily flex, but not that much. Clamp it, or hold it to the side of a table so it overhangs . Suspend a mass above the end of the ruler from zero height - that is, the mass is just kissing the ruler. Let go of the mass. You'll observe that the ruler deflects and vibrates. It'll deflect up to two times the deflection of the 'steady-state ' deflection. The ruler wasn't hit, as 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. The same thing will occur if you slide the mass . Nevertheless because the total mass is now less, it'll vibrate less.
Certainly, no one would try to apply a step-change in acceleration to a mechanical system if they knew it might vibrate? Well, you would be surprised.
Getting back to your neck; playground rides control jerk very closely. Otherwise the designers would be subject to court actions not to the motion.
So, a bit about Jerk - the crucial motion design parameter that immensely influences vibration of machine components. The motion design software in-built to MechDesigner allows you to edit Jerk values to any particular value you need.
About the Author:
Dr Kevin J Stamp is a Director of PSMotion Ltd, who focus on machine design software. PSMotion have developed MechDesigner to help design, scritinize and optimize multi-axis machines with complex motions. Kevin is a Mechanical Engineer with a PhD in High Speed Packaging Machine Design and 20 years expertise in improveing the performance of packing machinery. PSMotion Limited is based near Liverpool in the UK and was founded in 2004.
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