Assuming it is a steady state acceleration (or ramp from 0 very slowly up to the final constant acceleration) with no transient sloshing around, then you can solve it as follows.
1 - For the stationary case (gravity force but no horizontal acceleration), determine what angle could you tilt the glass without spilling.
2 - What level of horizontal acceleration when vectorially combined with gravity "acceleration" will give a total acceleration in a direction that satisfies the angle of tilt calculated in part 1.
Have you considered height of fluid compared to height of cup? Have you considered frequency range (F-min. and F-max.)? A quick experiment on my half-filled (or half-empty) coffee mug showed that tapping/impacting with my finger knuckle (closed fist) produced minor sloshing as compared to slight shaking of cup with my hand that produced considerable sloshing. I believe the g-level was much higher in the first case. I could measure it! Fluid in cup or tank has a sloshing natural frequency, so the frequency range of the applied acceleration along with amplitude should be considered.
Are you actually transporting half full cups of water or just using that as an example.
Maybe look at what sushi restaurants do for their revolving conveyor of food....
Or restaurants when you place the tray on a moving conveyor.
I think though this is the sort of thing that needs some experimentation as there seem to be many variables involved (weight of the cup, friction, how full the cup is, whether a truly "smooth start / stop can be applied ( see flywheel issue below) final speed of the conveyor etc)
You probably need a big flywheel on the motor drive so that it can't accelerate or decelerate very quickly.
How fast does the conveyor go when it reaches max speed?
Is there an issue in doing this ramp up / down over 10 seconds, or 20 or 30?
Remember - More details = better answers
Also: If you get a response it's polite to respond to it.
yeah I am working on it now, but the calculations are taking much much longer as the shape of the glass is not as simple as a rectangular tank or cylinder.
As has been said, for this Jerk is what matters (rate change of acceleration)
Yes you will have a max acceleration, but how quickly it changes matters more in this case.
for the cup volume I get .7L ... average 3" dia, 6" high = 42in3 = 700cc
what constrains the water to have the same CL when deflected ? is the volume above = the volume below the original water level ? doesn't look like it (if the center stays in the same place.
we know the initial freeboard, we know the initial empty volume of the cup. This is still the empty volume with the water tilted.
another day in paradise, or is paradise one day closer ?
goutam_freelance , great work! I was able to calculate the height of the water, but nothing more. Could you please explain how you drove the equation you used to solve for tan (alpha)?
