Calculating Valve Size With a Hydraulic Accumulator

[Big Tommy C]

Hello, Hope everyone is doing well.

I have a personal project I am working on and am trying to figure out the nature of the hydraulic system. I want to size a valve to the system properly and have been reading a lot about the Cv value. I don't fully understand how to implement this value into useful information and it may not be relevant to my application because this is a static value, but I will provide an example of my systems operating conditions.

The system will charge to a known value say 3000psi before the cycle begins. Each cycle will have to reach this value before it is allowed to begin.
The system also contains a hydraulic accumulator, I know the discharge volume per 100 psi drop in pressure.
When the cycle begins a logic valve will be vented and open, I can dictate the speed at which it opens but cannot easily meter the valve, it will switch to the fully open position, I can simply delay the open rate.
As the actuator moves the system pressure will drop quickly, the pump will not provide anywhere near enough flow to sustain pressure the accumulator will effectively be the prime mover during this period.
The actuator must be accelerated to a known final velocity over a known displacement, this also provides a known volume of oil that will need to be displaced.
I can also calculate the pressure drop on the supply side of the system if I displace the actuator over a known time.

I am trying to determine what size valve I should use to give me the flow I need to achieve the acceleration required.
I know as my pressure drops my flow will be equally effected, and I know the pressure differential on the valve will also effect flow. Any change in flow will change my rate of acceleration. So I am kinda stuck at this point I think I need a pressure differential to determine a valve size?

I think that ultimately since my acceleration will never be constant I will have to start with a higher acceleration and end with a lower acceleration to get and average acceleration that will provide my final velocity?

Example

 

[jrmichler]

trying to figure out the nature of the hydraulic system.

Interesting project, but first, it's time to back up a little. Start with a simplified hydraulic schematic using standard hydraulic schematic symbols. Search term, if needed, is hydraulic symbols. The simplified schematic below is what I think you have in mind:

Second, you need to define the operation:
Are you moving significant inertial mass?
Does the load have a significant friction force?
Does the load have a gravity component?
Does the load include an external force other than gravity?
How far is the move?
What is the required move time?

The valve Cv gives you the pressure drop at any flow rate. The actual calculations are iterative, and require enough computation that you are advised to write a simulation program. This can be done with a spreadsheet. The program is roughly as follows:

1) At start (T = 0), cylinder velocity and position are zero, and valve position is open. Since cylinder velocity is zero, flow velocity is zero, so P1 = P2 and P3 = 0. The difference between P2 and P3 applies a force to the piston. The sum of the forces on the piston causes an acceleration.
2) At time T = T + ##\Delta##T, the velocity is velocity at T + acceleration * ##\Delta##T, and cylinder position is position at T + velocity * ##\Delta##T. Now that you have a velocity and position, calculate P1, P2, and P3.
3) Repeat Step 2 until the cylinder reaches end of stroke.
4) Adjust parameters, such as valve Cv, until the simulated system works as desired.

Make the ##\Delta##T a variable, because you will need to adjust to get reasonable compromise between run time and accuracy. The general rule is start large, then decrease in steps until the answer stops changing. Simple Euler integration is normally good enough for this type of problem.

Unless, of course, the load inertia is low. In that case, the flow is determined by P1 and the valve Cv. Don't forget that the oil flows through the valve in two directions, so you have two pressure drops.

 

[Big Tommy C]

jrmichler, thank you for the reply.

This is not quite the valve configuration I have provided an example below.

The valve will only flow in one direction, using the logic valve circuit will allocate one valve to extend and one to retract on each port, 4 vales total for 2 directional movement. As far as the questions you have listed, the answer is yes on a lot of those, yes it has a gravity factor, yes its a substantial mass 5k lbs, it moves 3 feet, the only external force besides gravity will be the cylinder, it moves very quickly, about .250 milliseconds.

I have already calculated all the forces and flow rates and the gravity into what my final acceleration and acceleration time are going to be. My stuck point is actually finding a valve that will give me the flow I need and because the cycle time is so fast there isn't a way of providing a constant pressure, the pressure will inevitably drop so I need to find the balance point to get my final velocity.

I will certainly look into the spreadsheet, I was actually reading about spreadsheets beforehand but have yet to use one. Where exactly does the delta T fall into the equation? P3 will be negligible as an oversized dedicated valve can be implemented on each side of the cylinder for return.

EDIT*

It may also be worth noting, this is the datasheet providing me with valve selection options, I don't think I can develop a baseline IE a max flow or Qmax at 3000 psi pressure differential.

 

[Baluncore]

I have already calculated all the forces and flow rates and the gravity into what my final acceleration and acceleration time are going to be. My stuck point is actually finding a valve that will give me the flow I need and because the cycle time is so fast there isn't a way of providing a constant pressure, the pressure will inevitably drop so I need to find the balance point to get my final velocity.

If you know the; 1. Port size of the accumulator. 2. Port size of the actuator. 3. Peak flow rate. Then you know the diameter of the hydraulic line.
It should be easy to select an appropriate size of valve that will fit.

I assume the accumulator is separated from the actuator by a short hard line.
What type of valve do you need? A hydraulically operated ball valve would be the fastest with direct unobstructed flow.

 

[jrmichler]

THIS IS IMPORTANT: PF has a policy about dangerous activities: https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/. Review it. Now. Then show us how you plan to move this mass at this speed safely. Include all necessary calculations to convince us that you know what you are doing. This is a requirement, not a suggestion.

Some observations and recommendations:

When you are working with a 250 msec move, the time to shift the directional control valve, plus the time to shift the pilot operated valve becomes significant. That time should be included in your simulation.

If you use a constant acceleration move, the force will be about 30,000 lbs. A constant acceleration move accelerates for 125 msec, then decelerates for 125 msec. Those times do not include valve shifting time. Any other motion profile will have higher peak force.

Your circuit shows no provision to decelerate the load. If you are under the impression that you can stop the load by the cylinder reaching end of stroke, think again. Do the calculation: estimate the speed at end of travel, estimate deceleration distance, and calculate the force. Short answer is that the cylinder will be instantly destroyed.

How to do a dynamic system simulation using a spreadsheet.
Simplified example below:

The simulation starts at Time = 0 (cell A8). The time steps are incremented down Column A. The acceleration at each time step is calculated from the mass in cell B4, and the force in cell B5. In your case, you will calculate the force at each time step. The velocity at each time is simply the velocity at the previous time step plus the acceleration at that time step times the Delta T. Example: C9 = C8 + $B$3*B9. Similarly, the position is the position at the previous time step plus the velocity times the Delta T. Example: D9 = D8 + $B$3*C9. You copy the cells down until the position reaches the desired distance. If you use a smaller time step, copy more cells down. Note that this is the simplest possible integration, but it is good enough for this application.

For the numerical analysis types: The above code resulted in 3.4% position error at 0.3 seconds with 0.01 second Delta T, and 1.7% error at 0.3 seconds with 0.005 second Delta T. That's more accurate than the other numbers going into these calculations, so is good enough for this problem. It's also simple and easy to understand for somebody just getting into simulations.

Actual experience (not me, but I heard about it from one who was there): The engineering team designed a machine subassembly of about 2000 lbs mass. They connected it to a large hydraulic rotary actuator to rotate it 180 degrees, then a short delay, then rotate back. They correctly sized the actuator to accelerate and rotate the mass in the desired time (less than one second), but neglected to design a system to decelerate it. Testing was cut short to meet a management demand to ship the machine. In the customer plant, with the customer watching, it rotated and sheared off the entire bolt circle attaching it to the rotary actuator when it reached end of stroke. The entire 2000 lbs dropped about 5 feet and destroyed the rest of the machine. The customer was more than a little unhappy.

 

[Big Tommy C]

jrmichler

This project is still in the theoretical stage, I have yet to do stress simulations thus far as I am still trying to understand the math behind solving the valve size issue.
I completely understand the concern about the energy produced, the application is designed to transfer the kinetic energy of the mass into another mass by striking it, my calculations only produce 20000 ft lbs at this point because the hydraulic system will not accelerate the mass for the full 3 feet, it will cut into a neutral position at approximately 18 inches. This is my target force.

The cylinder will effectively be free moving no longer driven or held by hydraulics at the 18 inch point and will be dampened with an elastomer at the link point on the mass to prevent shock to the physical components when the mass strikes the intermediate plate between the mass and the object being struck, the intermediate plate will also have a sacrificial cushion material within it to prevent metal on metal contact.

The cylinder will NOT in any way shape or form contribute to decelerating the mass.
I have already researched the response times of the switching valves I plan to use, I can also change the logic valve open and close time by implementing orifices.

All of the data relating to acceleration, force required, system pressure, surface areas, fluid velocity, ect has been done, I will post it when I get some time to get it all together.

My main issue is just figuring out the valve size, The accumulator will deliver a very large flow and I think the valve will have to act as a flow control as well as a directional valve, I would prefer to create a pressure differential at first to slow the acceleration down vs opening a larger valve for less time I believe this will help with the response time of the valves and the overall stress of the components.

 

[Big Tommy C]

These are the parameters I have.

Mass 5000lbs
Final velocity at 18 inches 8.714 MPH with an acceleration of 16.5956 m/s2 in 0.234732 seconds

Free fall point 18 to 36 inches initial velocity of 8.714 MPH with and acceleration of 9.8 m/s2 creates a final velocity of 10.99 MPH in 0.103823 seconds to create a force of 20,187.96 FT LBS

Total fluid to displace in 18 inches 0.39779 Gallons Approximate flow required 101.67 Gallons per minute.

Pressure drop during this cycle time including pump supplied flow of 30 GPM is approximately 450psi

Force required 3464.79 ft lbs, this is because the acceleration will be downward so gravity will be assisting.

Minimum system pressure required to exert force 679psi

Bore Dia 100mm or 3.937", Rod Dia 72.6mm or 3"

System start operating pressure 3000psi, Accumulator precharge 1500psi Accumulator volume 5 gallons <-- I may change this at some point.

 

[Baluncore]

Final velocity at 18 inches 8.714 MPH with an acceleration of 16.5956 m/s2 in 0.234732 seconds

You have really made it difficult with all those discordant units.
If you use SI = System International, then there will be no weird coefficients.

Please use kg, rather than lbs.
Please use metre or mm, rather than inches.
Please use metre/sec, rather than MPH.
Please use m³ (or litre), rather than gallons. (Which may be either US or imperial).
Please use MPa or bar, rather than psi.

A force of 20,187.96 FT LBS should be 20,187.96 lbs force. FT LBS might be torque or energy. Better still specify the force in Newtons. A mass of 1 kg on Earth's surface weighs 9.8 N.

Hydraulic energy and power are easy to calculate if you stick to volume in m³ and pressure in pascals, kPa or MPa.

 

[jrmichler]

There is more to this than simply sizing a valve. That's why I am deliberately ignoring the valve sizing for now. Your posts so far are not consistent.

In Post #3, you state that you want to move 5,000 lbs mass a distance of 36 inches in 250 msec. That statement implies that the mass starts at position 0 at zero speed, and finishes at position 36 inches at zero speed. Such a move, if made with minimum acceleration, would accelerate at constant acceleration for the first 18 inches, then decelerate at the same acceleration for the last 18 inches. The acceleration would be 2300 in/sec^2, and the peak velocity 288 in/sec (24 ft/sec).

In Post #6, you mention kinetic energy and 20,000 ft-lbs in the same sentence, along with accelerating for 18 inches. The kinetic energy of 20,000 ft-lbs equates to a velocity of 16.0 ft/sec with 5,000 lbs mass.

In Post #7, you accelerate the mass to 12.8 ft/sec in 18 inches. Then you mention further acceleration by gravity. Some other numbers within that post are not consistent. This is unclear.

You need to clearly communicate what you are trying to do. A diagram here would be easily worth the proverbial 1000 words. Give us a diagram. It's easy to do - a hand sketch, photograph with a camera or scan with a scanner, save to your computer as a JPEG, then click the Attach files button under the reply window. Communicate to us exactly what you are trying to do with this mass, because each of your posts has the mass accelerated to a lesser velocity. Or we could simplify the problem by extrapolating 24 ft/sec to 16 ft/sec to 12.8 ft/sec to zero speed in a few more posts, in which case there is no problem to solve because the mass never moves.

I'm using English units because that's what I'm familiar with, even though SI units are better. Either system works, but please do not mix units. Mixing units is a recipe for problems. And please please round off to an appropriate precision.

Keep in mind that you are working with a serious amount of both momentum and kinetic energy.