Motion designers plan the intended sequence of 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. Usually the transient is obvious as a 'residual vibration' after an index, for instance. However,, all mechanisms vibrate during and after a motion, even if not obvious. The level of vibration largely determines the machine's capability, speed capacity, lifespan, MTBF, cost, etc.
The machine's response to a motion depends on the motion provided for it. If the motion response is poor, efforts are typically made to reconfigure the parts rather than redesign the motion. Redesigning parts is sometimes expensive and may put schedules back. With servos, redesigning the motion is free and can be done right away.
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 speed. Your head is being forced outwards with a constant acceleration. You may know your neck muscles must strain to keep your head upright at a constant 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, so long as the machine component is sufficiently strong enough to 'take the strain ', it'll often be strong enough for ever.
Packaging machines have parts that move backwards and forwards, jumbled together with dwell periods. Thus, machine parts are subject to random acceleration, not constant acceleration. Random acceleration means we've got 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 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 fast the muscles must stiffen.
A mechanical part will continually change its deflection proportionally to the acceleration it is the subject of. Won't it? Yes and No! Yes: if the jerk is 'low'. And no: if the jerk is 'high'.
What is 'low' and 'high'? Imagine the acceleration changes from 'Level 1' to a 'Level 2'. Level Two could be greater or less than Level One. If the acceleration is changed from Level One to Two at a 'low rate', the deflection of the component will 'more or less' be proportionate to the immediate acceleration. If it's 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 One to 2. Complicated?
It is less complicated to look at the speediest 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 respond to an acceleration that is meant to change in zero time. The deflection of all elements will first lag and then overshoot. They'll vibrate. By how much?
Try doing this. Take a steel ruler - one that will 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 - so that the mass is just touching the ruler. Let go of the mass. You may observe the ruler deflects and vibrates. It'll deflect up to twice the deflection of the 'steady-state ' deflection. The ruler was not hit, as the mass was at first 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 . Nevertheless 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; playpark rides control jerk really 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 in-built to MechDesigner allows you to edit Jerk values to any specific value you require.
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.