Motion designers manipulate the sequence of movements of parts in machines. As you would expect, the parts in the machine always react to the planned motion. The response nominally has two components: the steady state and the transient. Frequently the transient is obvious as a 'residual vibration' after an index, for example. However,, all mechanisms vibrate during and after a motion, even if not obvious. The level of vibration mostly determines the machine's efficiency, throughput, lifespan, MTBF, cost, etc.
The machine's reaction to a motion depends on the motion design for it. If the motion response is bad, efforts are commonly made to redesign the machine parts rather than redesign the motion. Redesigning parts is often expensive and can put 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 velocity. Your head is being forced outwards with a constant force. You'll know your neck muscles 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 overhangs the top of the chair's back-rest; it deflects to a consistent position. However, as long as the machine component is strong enough to 'take the strain ', it'll typically be robust enough forever.
Packaging machines have parts that can move back and forth, jumbled together with dwell periods. Hence, machine parts are subject to varying acceleration, not continual acceleration. Random acceleration means we have to study at Jerk. Jerk is therate-of-change of acceleration.
Let's say the centrifuge is speeding up. Consider the increase in radial acceleration, and pay no attention to 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 swiftly the neck muscles must stiffen.
A mechanical component will constantly change its deflection proportionally to the acceleration it is subjected to. Won't it? We'', 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 One' to a 'Level 2'. Level Two might 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 part will 'more or less' be proportionate to the immediate acceleration. If it is 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 less complicated to look at the swiftest 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 inertia can make a response to an acceleration that is meant to change in zero time. The deflection of all mechanical parts will lag and then overshoot. They'll vibrate. How much?
Try this experiment. Take a steel ruler - one that can simply bend, but not too 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 touching the ruler. Let go of the mass. You will observe the ruler deflects and vibrates. It will deflect up to twice the deflection of the 'steady-state ' deflection. The ruler was not hit, as 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. The same will happen if you remove the mass . However , as the total mass is now less, it'll vibrate less.
Certainly, nobody would try to apply 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 legal actions not to the motion.
Hence a bit about Jerk - the significant motion design parameter that significantly influences vibration of machine elements. The motion design software in-built to MechDesigner enables you to edit Jerk values to any specific value you need.
About the Author:
Doctor Kevin J Stamp is a Director of PSMotion L.T.D, who specialize 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 Ltd is based near Liverpool in England and was formed in 2004.
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