Oscillation Speed max and average.

[rdebarbouille]

I need to calculate the maximum speed of an oscillating shaft.
The system is build with 2 perpendicular shaft.
See attached jpg of mechanism.
I would like to knows what formula I need to obtain the maximun speed of the oscillation shaft
Acceleration etc...
I guess that the length of the fork, the excentric value are important for this calculation.
My ultimate goal is to know the torque output.
Anyone can help please?

 

[btrueblood]

Attached jpg? ...

 

[IRstuff]

The maximum speed of most such things is dictated by the motor, not the structure

TTFN

FAQ731-376

 

[rdebarbouille]

Attached JPg of the mechanism for oscillation calculation

 

[btrueblood]

Umm...maybe you could attach a 2nd view, and/or be more descriptive of what the axes of rotation are, and how the linkage mechanism between the two objects operates (rack & pinion gear? Sliding link?).

 

[rdebarbouille]

The grey shaft is the input power and rotation.
The grey shaft has an excentric spherical bearing.
This bearing push on the fork and alloy the pink shaft to oscillate. I know that for each rotation I have a full oscillation.
I am not to sure how to write down the mechanical formula to describe the torque available onto the pink shaft depending on the the grey shaft orientation.
The angular speed of the pink shaft goes from 0 rad/s to a max speed that is a function of the input speed of the grey shaft, the excentric value and the fork lenght (oscillation angle). I am guessing that with no friction and no loss of power the input and output power are constant. I can get an average speed base on the angular rotation. But I am not sure on how to get the maximum speed.

 

[MintJulep]

You should be more concerned about how long the thing will last before the eccentric ball on the gray shaft falls off due to fatigue.

I am guessing that with no friction and no loss of power the input and output power are constant.

I'm guessing that that is a bad guess.

Your power transfer is at a point contact. The equations for the location and direction of the transfer vector are simple functions of the geometry. The power adsorbed by the output is a function of the second derivative of the oscillation. There's a bunch of friction that will be hard to characterize.

Ignoring friction, it looks like a relatively simple set of equations to solve.

 

[btrueblood]

"I am not to sure how to write down the mechanical formula to describe the torque available onto the pink shaft depending on the the grey shaft orientation."

Let T = input torque on the grey shaft.
e = eccentricity of the ball (centerline of ball to centerline of grey shaft)
Max force applied to fork when eccentricity is oriented parallel to axis of pink shaft = F = T/e
Min force on fork when eccentricity is perpendicular = 0.

I think you'll have a sin^2 variation in force, but I'd have to grind the geometry to be sure.

You might look at nutating pumps and their bearings to get some ideas.

 

[FeX32]

Look up "hookes joint" .
For example:

http://www.gwb-essen.de/industrie/english/seite_32.html

Gives geometric relations and equations.


Fe

 

[FeX32]

At first glance yours seems the same> unless you are trying for a CV.


Fe

 

[zekeman]

Basically, you have an eccentric cam with eccentricity e pushing an arm of length L.
So the end of the arm moves up and down

e*cos(wt) and the angular displacement is very close to

e*cos(wt)/L

And the angular speed would be the derivative of this angle or
e*w*sin(wt)

which is maximum when the sin rem is 1

Your answer is

wm=e*w/L

 

[zekeman]

Oh. the average over 1/2 cycle is
2/pi*wm=.636*wm

 

[Occupant]

Or use this -->

 

[zekeman]

Looking at your question regarding torque delivery, you need to know the load at the link, the inertias of the link and the driving system before it can be formulated.

If this is already designed then you are stuck with a less than ideal concept, unless the loads and inertias are fairly low, or you are willing to sacrifice life for simplicity.

The main problems are friction and wear Use of cams and ball bearing followers can make the design far better.

Why don't you post the total design requirements and then maybe you can get some better design direction.

The dynamics and torque transfer are the easy part.

 

[rdebarbouille]

Thank you for all your help.
The product is already on the market. I try to understand it a bit more to make sure I know the maximum force.

Thank you.