Calculating torque and angular acceleration
Calculating torque and angular acceleration
(OP)
Hello,
I've got a project that utilizes a diverter mechanism that will operate very quickly (one stroke in 0.094s). I need to calculate the cylinder size that will activate the diverter assembly fast enough. The diverter is basically a glorified flapper that pivots on one end and the other end moves up and down approximately 1". I've completed my calculations and wanted to attach them, but I'm not sure how to do that???
But, my "real" problem is that the force seems rather low. My methodology is as follows:
1) Calc cyl velocity from max time and cyl stroke (.094s/1")
2) Calc angular Vel. from cyl velocity (omega=V/r)
3) Calc angular acceleration from ang. vel. and total time (.094s) (alpha=omega/t)
4) Calc torque from ang. accel and Mass Mom. Inertia (T=I*alpha)
5) Calc cylinder force needed from torque and radius of moment arm.
Am I missing something?
I appreciate any help on this,
Craig Sink
Mechanical Engineer
Force Design, Inc.
I've got a project that utilizes a diverter mechanism that will operate very quickly (one stroke in 0.094s). I need to calculate the cylinder size that will activate the diverter assembly fast enough. The diverter is basically a glorified flapper that pivots on one end and the other end moves up and down approximately 1". I've completed my calculations and wanted to attach them, but I'm not sure how to do that???
But, my "real" problem is that the force seems rather low. My methodology is as follows:
1) Calc cyl velocity from max time and cyl stroke (.094s/1")
2) Calc angular Vel. from cyl velocity (omega=V/r)
3) Calc angular acceleration from ang. vel. and total time (.094s) (alpha=omega/t)
4) Calc torque from ang. accel and Mass Mom. Inertia (T=I*alpha)
5) Calc cylinder force needed from torque and radius of moment arm.
Am I missing something?
I appreciate any help on this,
Craig Sink
Mechanical Engineer
Force Design, Inc.





RE: Calculating torque and angular acceleration
from steps 1) and 2) you're assuming a constant velocity
which implies an infinite acceleration at both ends of the travel.
maybe you need to assume a real acceleration value and check that you get the required displacement in the time allowed.
does this flipper flip one way (from a starting point to a finsihing point) or both ways (start-end-back to start) in one activation ?
is anything being deflected by the flipper ?
RE: Calculating torque and angular acceleration
You need to write the complete differential equations for the system (control valve dynamics, fluid flow dynamics, instant pressure inside the cylinder, system inertia's, friction etc.) and solve it.
You assume constant cylinder force but this is not the real thing. While the cylinder moving a fluid flow in and the pressure in the cylinder varies. The valve that command the fluid to the cylinder has a time constant too.
Depends on the flow rates and the fluid pressure the valve time constant may even be larger than the cylinder time constant.
By the way it should be 1) Calc cyl velocity from max time and cyl stroke (1"/.094s).
RE: Calculating torque and angular acceleration
Yes, step 3 is a problem. I realized that I need to calculate the acceleration from the final velocity, not the average. E.g. my avg V would be 1/2 of the final V if accel is constant.
EX:
s = 1" (travel)
t = 0.094s
V_avg = 1"/0.094s
V_initial = 0in/s
V_final = (1/.094)*2
Accel = V_final/t
I will also take your suggestion to assume a real acceleration and work backwards as a check. In regards to the flipper, my calculations are for start to finish, no return as an activation.
Thank you,
Craig Sink
Mechanical Engineer
Force Design, Inc.
RE: Calculating torque and angular acceleration
RE: Calculating torque and angular acceleration
RE: Calculating torque and angular acceleration
1. The solenoid receives a voltage that energizes and magnetizes a coil. This coil takes a certain amount of time to magnetize due to the coil's inductance.
2. The magnetized coil pulls open the pilot valve.
3. Air rushes through the pilot, building pressure on the valve spool.
4. Once the pressure is great enough it pushes the spool to the opposite end of its travel, opening both the path from the supply port of the valve to the inlet port of the cylinder and the path from the exhaust port of the cylinder to the exhaust port of the valve.
5. Pressure in the rod side of the cylinder begins to vent out the exhaust port of the valve while pressure builds in the piston side. Fluid mechanics dictate the speed with which the air can exhaust from the rod side and fill the piston side.
6. When pressure in the piston side rises above the falling rod side pressure the cylinder begins to move. During this time the output force rises as the differential between piston and rod sides. Even if the rod side started out with zero (gage) pressure, the piston side still has to force all the atmospheric air out as it travels. With the speed you're looking at, this will likely be a factor.
There are a few ways you can attempt to reduce the impact of these factors:
1. Use a spring return cylinder if possible, and drill out its rod side port to a rather large size.
2. Choose a cylinder that has large ports to start with.
3. Choose a large valve with low restriction.
4. Minimize all piping runs, especially between valve and cylinder.
5. Make sure supply lines are large up to the valve.
6. Use as high of pressure as you can.
I'm guessing this is a low-volume, one-off type design rather than a consumer product design. Rather than setting up all the equations as suggested by israelkk, in your shoes I would probably do as much real-world testing as possible. If you're using off-the-shelf components they are all rather inexpensive compared to design time labor hours.
RE: Calculating torque and angular acceleration
In regards to the additional factors such as valve delay and fluid flow, etc. Those factors don't necessarily have to happen within the specified time. The need to actuate the diverter will be determined ahead of time by the controls so the actuation could [i]begin[\i] early-if that makes sense! My calculations are to determine the proper cylinder size such that the cylinder can operate in the given time constraints. As Handleman mentioned, there will be real world testing and adjustment done rather than modeling the entire system and calculating from there (we don't have the privilege of doing that, unfortunately).
That said, I appreciate all of the input.
Craig Sink
Mechanical Engineer
Force Design, Inc.
RE: Calculating torque and angular acceleration
RE: Calculating torque and angular acceleration