Motion designers choreograph the movements of parts in machines. As you might expect, the parts in the machine always react to the intended 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, as an example. Nevertheless, all mechanisms vibrate during and after a motion, even if not visible. The scale of vibration principally determines the machine's MTBS, throughput, lifespan, MTBF, cost, for example.
The machine's reaction to a motion depends on the motion designed . If the motion response is poor, 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 cost free and can be done immediately.
Let's imagine 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 speed. Your head is being flung outwards with a constant force. You'll know must strain to keep your head upright at a continual position relative to your shoulders.
Now picture 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. Nevertheless, so long as the machine part is sufficiently strong enough to 'take the strain ', it'll usually be powerful enough forever.
Packing machines have parts that can move forwards and backwards, mixed together with stationary periods. Thus, machine parts are subject to varying acceleration, not constant acceleration. Random acceleration means we must study at Jerk. Jerk is the rate of change of acceleration.
Let's imagine the centrifuge is speeding up. Think of the increase in radial acceleration, and forget the tangential acceleration. Your neck muscles are in the process of 'exerting themselves more' to keep your head in one position. They are feeling 'Jerk'. The muscles in your neck 'feel ' the rate of change of acceleration as they are able to 'feel ' how quickly the neck muscles must stiffen.
A mechanical element will constantly change its deflection proportionally to the acceleration it is the subject of. Won't it? Yes and No! Yes: if the jerk is 'low'. 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 2 might be greater or less than Level 1. If the acceleration is modified from Level 1 to 2 at a 'low rate', the deflection of the component will 'more or less' be proportionate to the immediate acceleration. If it is 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 Two. Complicated?
It is easier to look at 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 inertia can respond to an acceleration that is meant to change in zero time. The deflection of all mechanical parts will first lag and then overshoot. They'll vibrate. By how much?
Try this experiment. Take a steel ruler - one that can simply bend, but not that 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 notice the ruler deflects and vibrates. It will deflect up to two times the deflection of the 'steady-state ' deflection. The ruler wasn't hit, because the mass was at first touching the ruler. The ruler was only subject to a step change in force - equal to a step-change in acceleration. A similar thing will occur if you remove the mass . Nevertheless because the total mass is now less, it'll vibrate less.
Certainly, 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 really closely. Otherwise their designers would be subject to legal actions not to the motion.
Therefore a bit about Jerk - the important motion design parameter that significantly influences vibration of machine parts. The motion design software built in to MechDesigner allows you to edit Jerk values to any particular value you want.
About the Author:
Dr Kevin J Stamp is a Director of PSMotion Ltd, who focus on machine design software. PSMotion have developed MechDesigner to help design, scritinize and optimize multi-axis machines with complex motions. Kevin is a Mechanical Engineer with a PhD in High Speed Packaging Machine Design and 20 years expertise in improveing the performance of packing machinery. PSMotion Limited is based near Liverpool in the UK and was founded in 2004.
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