Motion designers manipulate the movements of parts in machines. As you'd expect, machine parts always respond to the proposed 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. Nonetheless, all mechanisms vibrate during and after a motion, even when not obvious. The scale of vibration mostly determines the machine's efficiency, throughput, lifespan, MTBF, cost, for example.
The machine's response to a motion depends on the motion input for it. If the motion response is poor, efforts are commonly made to reconfigure the parts instead of redesign the motion. Redesigning parts is sometimes costly and may put project schedules back. With servos, redesigning the motion is cost free and can be carried out right away.
Let's envisage the machine part is your head, blind-folded, 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 must strain to keep your head upright at a constant position relative to your shoulders.
Now picture 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. However, as long as the machine component is sufficiently strong enough to 'take the strain ', it'll typically be powerful enough forever.
Packaging machines have parts that move forwards and backwards, jumbled together with still periods. Therefore, machine parts are subject to varying acceleration, not constant acceleration. Varying acceleration means we've got to study at Jerk. Jerk is therate-of-change of acceleration.
Let's imagine the centrifuge is speeding up. Consider the increase in radial acceleration, and forget the tangential acceleration. The muscles in your neck are in the procedure of 'exerting themselves more' to keep your head in one place. They are feeling 'Jerk'. The muscles in your neck 'feel ' the rate of change of acceleration as they will be able to 'feel ' how swiftly the neck muscles must stiffen.
A mechanical part 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'. No: if the jerk is 'high'.
What is 'low' and 'high'? Imagine the acceleration changes from 'Level One' to a 'Level Two'. Level Two might be greater or less than Level 1. If the acceleration is modified from Level One to Two at a 'low rate', the deflection of the part will 'more or less' be proportional to the immediate acceleration. If it is a 'high rate', the deflection of the part 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 simpler to look at the fastest imaginable 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 intended to change in zero time. The deflection of all mechanical components will first lag and then overshoot. They'll vibrate. By how much?
Here is an experiement. Take a steel ruler - one that can easily flex, but not that much. Clamp it, or hold it to one 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. Release the mass. You'll notice the ruler deflects and vibrates. It'll deflect up to two times 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 - equal to a step-change in acceleration. The same thing will occur if you remove the mass off the ruler. Nevertheless because the total mass is now less, it will vibrate less.
Certainly, nobody would try to use a step-change in acceleration to a mechanical system if they knew it would vibrate? Well, you might be surprised.
Getting back to your neck; playground rides control jerk extremely closely. Otherwise their designers would be subject to legal actions not to the motion.
Hence a bit about Jerk - the important motion design parameter that significantly influences vibration of machine components. 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 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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