Motion designers direct the movements of parts in machines. As you'd expect, machine parts always respond to the planned motion. The response nominally has two components: the steady state and the transient. Usually the transient is obvious as a 'residual vibration' after an index, for instance. Nonetheless, all mechanisms vibrate during and after a motion, even if not obvious. The level of vibration mostly determines the machine's performance, speed, life, MTBF, life cycle cost, and so on.
The machine's reaction to a motion depends on the motion design . If the motion response is bad, efforts are typically made to reconfigure the machine parts rather than redesign the motion. Redesigning parts is often costly and put project schedules back. With servos, redesigning the motion is free and can be done instantly.
Let's envisage 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 flung outwards with a constant force. You'll know your neck muscles must strain to keep your head upright at a constant position relative to your shoulders.
Now imagine 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. Nevertheless, as long as the machine component is strong enough to 'take the strain ', it will often be robust enough forever.
Packing machines have parts that can move forwards and backwards, mixed together with dwell periods. Therefore, machine parts are subject to random acceleration, not constant acceleration. Random acceleration means we have to take a 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 pay no attention to the tangential acceleration. The muscles in your neck are in the process 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 as they will be able to '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? 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 1. 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 is a 'high rate', the deflection of the part will first 'lag', then 'catch up' and, if there is little damping, 'overshoot' and then repeat. This is both during and after the acceleration transition from Level 1 to Two. Complicated?
It is simpler to consider the speediest possible 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 mechanical elements will lag and then overshoot. They'll vibrate. By how much?
Why not try this. Take a steel ruler - one that will easily 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 - that is, the mass is just kissing the ruler. Let go of the mass. You will observe the ruler deflects and vibrates. It'll deflect up to twice 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 - identical to a step-change in acceleration. A similar thing will happen if you slide the mass . Nonetheless because the total mass is now less, it will vibrate less.
Surely, 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; playpark rides control jerk very closely. Otherwise their designers would be subject to legal 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 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.