Parallel leaf spring motion

[geoffthehammer]

I have a mechanism incorporating two parallel leaf springs that suspend a mass. The mass is being vibrated (in the weak direction) at up to 100Hz with a small amplitude by an actuator. We are experiencing errors of motion in the direction perpendicular to the direction of oscillation.

Can anyone point me in the right direction to get information regarding calculating the off-axis errors of motion caused by factors such as manufacture/build errors, out of balance masses and offset actuation?
I realise that the errors are going to be small but I am looking to get the errors down to less than 10 microns

 

[rb1957]

"errors" ? if you modelled the mechanism, then maybe the modelling might cause errors in the output; but it sounds like you have a physical prototype, in which case i'd say you're getting unexpected results (rather than errors).

if everything is perfectly symmetrical then there'd be no out-of-plane defelections. so something must be unsymmetrical (but then i expect you're up to here already!). of course, if the load is not applied precisely on the CL, then there'll be out-of-plane motion. if the load is precisely on CL (a pretty amazing accomplishment), then maybe the restraint (the clipping between the leaves, or their attmt to "the rest of the world" isn't precisely symmetrical then you'd get out-of-plane motion.

good luck

 

[Barry1961]

Interesting problem.

As the mass moves the leaf springs will either get longer or shorter in relation their mounts. If you use the standard mounting with one fixed and one floating you will always get a side ways movement which can be calculated. If you fix both ends you will induce a twist which is not so easily calculated. If you leave both ends floating you need some external linkage and/or guidance.

I don’t have an answer but I do admire the problem.

Barry1961

 

[geoffthehammer]

rb1957:
Unfortunately the mass is by necessity off centre. I am trying to predict what out of plane deviations that causes. If it can be predicted we could modify the point at which the driving force is applied or perhaps change the depth of the leaf springs to reduce the effect. I guess we could do it by trial and error but it would be nicer to have a theoretical approach to the problem.

Barry1961:
The leaf springs are both fixed at one end and both fixed to the movable mass at the other so that the actuating force deflects them (and the mass) sideways, so we have a sort of deformed parallelogram. Yes there will be some shortening effect but the deviations we are concerned about are in the third orthogonal direction

 

[rb1957]

if the driving mass is off-center, you are introducing a torque into the leaves, therefore getting out-of-plane deflections ... no error, and should be expected. how can the mounts react this torque ? torque applied to a solid element is easliy solved, the question in your problem, is how is the torque shared between the two leaves ? (presumably it is introduced equally ...

i'm sorry, if been re-reading your reply to Barry161, i had assumed that the load was applied transversly to the leaves (as tho' the spring was supporting an axle) ... but it sounds like your applying a tension force along the length of the spring (with the spring fixed at one end, and loaded (pulled) at the other) ?

let's sort this out first, is the spring a conventional axle spring (anchored at both ends, transversely loaded in the middle) or something different (anchored at one end, loaded (transversly or axially) at the other) ...

 

[geoffthehammer]

see the following plan view:

Fxxxxxxxxxxxxxxxxxxxxxx
F yy
F yy
F TTyyM
F yy
F yy
Fxxxxxxxxxxxxxxxxxxxxxx

Note this a plan view

F represents a plane to which the ends of the springs are fixed. The leaf springs are weak in the direction up and down the page (horizontal) but stiff in the direction into/out of the page (vertical).

YY represents a faceplate to which the outer ends of springs are fixed. M is a mass attached to the faceplate (symmetrical in the plan view as shown but not symmetrical in the vertical plane).

TT represents the driving force which deflects the springs up and down the page. We could position the driving force where we like.
Note that due to the shortening effect of the distorted spring, the mass will move slightly towards the fixed plane FFFF

The deviations (rather than errors) that we want to investigate are those in the vertical.

 

[rb1957]

so the leaf blades are normal to the screen,
we're looking at a plan view of the set-up, so gravity is acting into-the-screen,
the leaf baldes are cantilevered off to the left,
the tie-bar, between the leaves, is fixed at both ends,
the mass is mounted mid-way between the leaves (exactly?),
the driving actuator is mounted anywhere on the tie-beam, driving in the plane of the screen?
and (phew!) you're interested in deflections into the screen
(driven by gravity?)

 

[GregLocock]

How big is this thing 10 microns in a 100mm long unit could be fine, in a 10mm unit, not. How much axial deflection do you get?

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[geoffthehammer]

rb1957: In plan view, the mass is fixed in the centre of the face plate but in the elevation, the mass is slightly below the centreline. The driver can be mounted so as to act virtually anywhere and yes, it drives in the plane of the screen. The deflections/deviations we are interested in are those into the screen. Not necessarily caused by gravity but also by offset inertias and by small errors in manufacture of the components or buld innaccuracies. For example, say one leaf spring is tilted with respect to the other or slightly higher by 3-5 microns and so forth.

Greg: To give you some idea of size, the length of the leaf springs is approx 90mm. The width and height of the face plate is approx 80mm x 40mm. The amplitude of deflection (in the plane of the screen) is adjustable between +/- 0.25mm to +/- 0.75mm.
At an amplitude of +/- 0.5mm the deviations in vertical movement (into/out of the screen) that we currently experience are of the order of less than 5 microns at 20Hz rising to 50+ microns at 100Hz.

We use a calibrated eddy current distance sensor to measure the errors.

It does seem as though part of the problem is due to the offset mass, we could try balancing it by trial and error or we might try offsetting the driver but it would be nice to have some theory behind it all.

 

[rb1957]

the leaves are reacting the weight and the driven force as cantilevers, therefore deflecting out-of-plane.

and the drive motor is accelerating the mass, isn't it ?
so that the force on (and deflection of) the leaves is a function of dirve frequency, no?