Motion designers manipulate the sequence of 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, for instance. Nonetheless, all mechanisms vibrate during and after a motion, even if not observable. The amplitude of vibration principally determines the machine's OEE, throughput, lifespan, maintenance schedule, cost, for example.
The machine's reaction to a motion depends upon the motion input . If the motion response is bad, efforts are often made to reconfigure the machine parts instead of redesign the motion. Redesigning parts is often expensive and will put project schedules back. With servos, redesigning the motion is cost free and can be carried out instantly.
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 with a steady speed. Your head is being forced outwards with a constant acceleration. You'll know must strain to keep your head upright at a constant position relative to your shoulders.
Now imagine 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. However, as long as the machine part is sufficiently strong enough to 'take the strain ', it'll typically be powerful enough forever.
Packaging machines have parts that can move forwards and backwards, jumbled together with dwell periods. Therefore, machine parts are subject to varying acceleration, not continual acceleration. Random acceleration means we must 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 forget the tangential acceleration. Your neck muscles are in the process of 'exerting themselves more' to keep your head in one place. They're experiencing 'Jerk'. The muscles in your neck 'feel ' the rate of change of acceleration as they can 'feel ' how swiftly the neck muscles need to stiffen.
A mechanical component 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's 'low' and 'high'? Imagine the acceleration changes from 'Level One' to a 'Level Two'. Level Two might be larger or less than Level One. If the acceleration is changed from Level 1 to 2 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 component will first 'lag', then 'catch up' and, if there's little damping, 'overshoot' and then repeat. This is during and after the acceleration transition from Level One to 2. Complicated?
It is easier to look at 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 mass can respond to an acceleration that is designed to change in zero time. The deflection of all parts will first lag and then overshoot. They WILL vibrate. How much?
Try this experiment. Take a steel ruler - one that will easily flex, 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 - so that the mass is just kissing the ruler. Let go of the mass. You will observe the ruler deflects and vibrates. It will 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 - equivalent to a step-change in acceleration. A similar thing will happen if you remove the mass off the ruler. Nevertheless because the total mass is now less, it will 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; playground 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 massively influences vibration of machine parts. The motion design software built in to MechDesigner enables 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.
