Motion designers manipulate the intended sequence of 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. 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 amplitude of vibration largely determines the machine’s OEE, speed, life, MTBF, cost, for example.
The machine’s reaction to a motion depends on the motion design . If the motion response is bad, efforts are typically made to reconfigure the machine parts rather than redesign the motion. Redesigning parts is typically expensive and can put timetables back. With servos, redesigning the motion is free and can be done instantly.
Let’s imagine 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 velocity. Your head is being forced outwards with a constant acceleration. You may know your neck muscles must strain hard 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. However, so long as the machine component is strong enough to ‘take the strain ‘, it will typically be powerful enough for ever.
Packaging machines have parts that move backwards and forwards, mixed in with stationary periods. Therefore, machine parts are subject to varying acceleration, not constant acceleration. Varying acceleration means we’ve got to look at Jerk. Jerk is therate-of-change of acceleration.
Let’s imagine the centrifuge is speeding up. Consider only the increase in radial acceleration, and ignore the tangential acceleration. Your neck muscles are in the process of ‘exerting themselves more’ to keep your head in one position. They are experiencing ‘Jerk’. The muscles in your neck ‘feel ‘ the rate of change of acceleration because they will be able to ‘feel ‘ how quickly the muscles need to stiffen.
A mechanical component will constantly change its deflection proportionally to the acceleration it is subject to. Won’t it? 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 1’ to a ‘Level 2’. Level Two might be larger or less than Level One. If the acceleration is changed from Level 1 to Two at a ‘low rate’, the deflection of the element 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 is little damping, ‘overshoot’ and then repeat. This is both during and after the acceleration transition from Level 1 to 2. Confused?
It is less complicated to look at the fastest 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 make a response to an acceleration that is designed to change in zero time. The deflection of all components will first lag and then overshoot. They’ll vibrate. By how much?
Try this experiment. Take a steel ruler – one that will easily bend, 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 – that is, the mass is just kissing the ruler. Release the mass. You’ll see 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 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 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 would be surprised.
Getting back to your neck; playpark rides control jerk extremely closely. Otherwise their designers would be responding to lawsuits not to the motion.
Therefore a bit about Jerk – the crucial motion design parameter that immensely influences vibration of machine components. The motion design software built-in to MechDesigner lets you edit Jerk values to any particular value you want.
Dr Kevin J Stamp is a Director of PSMotion Limited, 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 Ltd is based near Liverpool in G.B. and was launched in 2004.