The Importance of Jerk in Motion Design for Machines
Motion designers manipulate the movements of parts in machines. As you'd expect, machine parts 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 obvious. The level of vibration mostly determines the machine's PE, capacity, life, MTBF, cost, for example.
The machine's response to a motion depends on the motion design . If the motion response is poor, efforts are commonly made to redesign the parts rather than redesign the motion. Redesigning parts is sometimes costly and can put project schedules back. With servos, redesigning the motion is free and can be carried out instantly.
Let's envisage the 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 constant speed. Your head is being flung outwards with a constant force. You may 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. However, so long as the machine part is sufficiently strong enough to 'take the strain ', it'll often be robust enough for ever.
Packing machines have parts that can move forwards and backwards, jumbled together with still periods. Therefore, machine parts are subject to random acceleration, not constant acceleration. Random acceleration means we must look at Jerk. Jerk is therate-of-change of acceleration.
Let's say the centrifuge is speeding up. Think of the increase in radial acceleration, and ignore the tangential acceleration. Your neck muscles are in the process of 'exerting themselves more' to keep your head in one place. They're experiencing 'Jerk'. The muscles in your neck 'feel ' the rate of change of acceleration because they can 'feel ' how quickly the muscles must stiffen.
A mechanical component 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'. And no: if the jerk is 'high'.
What is 'low' and 'high'? Let's imagine the acceleration changes from 'Level 1' to a 'Level Two'. Level Two might be greater or less than Level One. If the acceleration is changed from Level 1 to Two at a 'low rate', the deflection of the component will 'more or less' be proportionate to the immediate acceleration. If it is a 'high rate', the deflection of the element 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 2. Confused?
It is less complicated 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 definitely infinite.
Nothing with mass can respond to an acceleration that is meant to change in zero time. The deflection of all mechanical components will lag and then overshoot. They'll vibrate. How much?
Why not try this. Take a steel ruler - one that will 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 - so that the mass is just kissing the ruler. Let go of the mass. You may notice the ruler deflects and vibrates. It will deflect up to twice the deflection of the 'steady-state ' deflection. The ruler wasn't hit, because the mass was at first 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 happen if you remove the mass . However , as the total mass is now less, it'll vibrate less.
Certainly, nobody would try to use a step-change in acceleration to a mechanical system if they knew it might vibrate? Well, you might be surprised.
Getting back to your neck; playground rides control jerk very closely. Otherwise the designers would be responding to lawsuits not to the motion.
So, 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 need.
About the Author:
Doctor Kevin J Stamp is a Director of PSMotion Limited, who develop 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 Great Britain and was launched in 2004.
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