Importance of Jerk in Motion Design for Machines

By Dr Kevin J Stamp

Motion designers direct the movements of parts in machines. As you would expect, machine parts always react to the planned motion. The response nominally has 2 components: the steady state and the transient. Often the transient is obvious as a 'residual vibration' after an index, as an example. Nevertheless, all mechanisms vibrate during and after a motion, even when not obvious. The scale of vibration mostly determines the machine's OEE, throughput, lifespan, MTBF, cost, etc.

The machine's response to a motion depends on 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 typically costly and can put timetables back. With servos, redesigning the motion is free and can be done immediately.

Let's picture 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 velocity. Your head is being forced outwards with a constant force. You will know the muscles in your neck must strain 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 element is sufficiently strong enough to 'take the strain ', it will often be powerful enough for ever.

Packing machines have parts that move forwards and backwards, mixed together with dwell periods. Hence, machine parts are subject to random acceleration, not continual acceleration. Varying acceleration means we have to take a look at Jerk. Jerk is therate-of-change of acceleration.

Let's say 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 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 as they can 'feel ' how swiftly the muscles need to stiffen.

A mechanical element will constantly change its deflection proportionally to the acceleration it is subject to. Won't it? We'', yes and no! Yes: if the jerk is 'low'. And no: if the jerk is 'high'.

What's 'low' and 'high'? Imagine the acceleration changes from 'Level One' to a 'Level Two'. Level 2 could be larger or less than Level One. If the acceleration is modified from Level 1 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 both during and after the acceleration transition from Level 1 to Two. Complicated?

It is less complicated to consider the fastest possible rate of change of acceleration - infinite jerk. This is a step-change in 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 lag and then overshoot. They WILL vibrate. By how much?

Why not try this. Take a steel ruler - one that can simply flex, but not too much. Clamp it, or hold it on the side of a table so it overhangs the table. Suspend a mass above the end of the ruler from zero height - that is, the mass is just touching the ruler. Let go of the mass. You'll notice that the ruler deflects and vibrates. It'll deflect up to twice the deflection of the 'steady-state ' deflection. The ruler was not hit, because the mass was initially touching the ruler. The ruler was only subject to a step change in force - identical to a step-change in acceleration. A similar thing will occur if you slide the mass off the ruler. Nonetheless as the total mass is now less, it'll vibrate less.

Surely, 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; playpark rides control jerk very closely. Otherwise their designers would be responding to court actions not to the motion.

So, a bit about Jerk - the important motion design parameter that massively influences vibration of machine elements. The motion design software built-in to MechDesigner enables you to 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.