Motion designers direct the intended movements of parts in machines. As you might expect, the parts in the machine always respond to the planned motion. The response nominally has 2 components: the steady state and the transient. Often the transient is obvious as a 'residual vibration' after an index, as an example. However,, all mechanisms vibrate during and after a motion, even if not obvious. The amplitude of vibration mostly determines the machine's PE, speed capacity, life, MTBF, cost, etc.
The machine's response to a motion depends on the motion provided for it. If the motion response is bad, efforts are commonly made to redesign the parts instead of redesign the motion. Redesigning parts is typically costly and will 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, 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 acceleration. You may know your neck muscles 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, so long as the machine element is strong enough to 'take the strain ', it will usually be robust enough forever.
Packing machines have parts that move backwards and forwards, mixed in with stationary periods. Hence, machine parts are subject to varying acceleration, not constant acceleration. Random acceleration means we've got 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. The muscles in your neck are in the process of 'exerting themselves more' to keep your head in one position. They're feeling 'Jerk'. Your neck muscles 'feel ' the rate of change of acceleration because they are able to 'feel ' how swiftly the neck muscles need to stiffen.
A mechanical element will repeatedly 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's 'low' and 'high'? Imagine the acceleration changes from 'Level One' to a 'Level Two'. Level 2 might be greater or less than Level 1. If the acceleration is modified from Level One to 2 at a 'low rate', the deflection of the component will 'more or less' be proportional to the immediate acceleration. If it's 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 during and after the acceleration transition from Level One to 2. Confused?
It is easier to consider the swiftest conceivable 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 intended to change in zero time. The deflection of all elements will first lag and then overshoot. They WILL vibrate. By how much?
Try this experiment. 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 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 will see the ruler deflects and vibrates. It will deflect up to twice 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 - equivalent to a step-change in acceleration. The same will occur if you remove the mass off the ruler. Nevertheless 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 might vibrate? Well, you would be surprised.
Getting back to your neck; playpark rides control jerk extremely closely. Otherwise the designers would be subject to court actions not to the motion.
So, a bit about Jerk - the significant motion design parameter that massively influences vibration of machine parts. The motion design software built in to MechDesigner lets you edit Jerk values to any particular value you require.
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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