How to Calculate Input Torque for a Hydraulic Oscillating Ram Pump?

[Don Bori]

How can I get the Input Torque required to pump the double-acting cylinders with the following specifications below?

Ram Working Pressure = 2 bars
Ram ID = 100 mm.
Ram Stroke = 1,000 mm.

 

[jrmichler]

That looks more like a radial piston pump than a hydraulic ram pump. Hydraulic ram pumps use the inertia of moving water to generate pressure. I can think of two ways to calculate the torque:

1) Each piston has a force and a direction. Calculate the sum of moments about the crankshaft. Include a factor to account for friction. Or you could add friction at each bearing to the FBD.

2) Given the displacement, find the volume pumped per revolution. From the volume per revolution and the pressure, and assuming an RPM, calculate the power required. Knowing the power and RPM, calculate the torque. Or combine the two equations and calculate the torque directly from the displacement and pressure. Include a factor to account for friction.

Best is to do it both ways to cross check your results.

 

[Baluncore]

Welcome to PF.

With a stroke of 1000 mm the virtual crank will have a radius of 500 mm = 0.5m;
The area of the piston is Pi * (50mm)^2 = 7854 mm2 = 0.007854 m2;
2 Bar = 2 * 100 kPa = 200 kPa;
Piston force = 200 * 7.854 Newton = 1570.8 N;
Torque will be 0.5 m * 1570.8 N = 780 Nm.

Terminology confusion, see; https://en.wikipedia.org/wiki/Hydraulic_ram

 

[Don Bori]

Thanks jrmichler, it was good to confirm from you that I have to consider all the forces from each cylinder acting on the crank-lobe.

That looks more like a radial piston pump than a hydraulic ram pump. Hydraulic ram pumps use the inertia of moving water to generate pressure. I can think of two ways to calculate the torque:

1) Each piston has a force and a direction. Calculate the sum of moments about the crankshaft. Include a factor to account for friction. Or you could add friction at each bearing to the FBD.

2) Given the displacement, find the volume pumped per revolution. From the volume per revolution and the pressure, and assuming an RPM, calculate the power required. Knowing the power and RPM, calculate the torque. Or combine the two equations and calculate the torque directly from the displacement and pressure. Include a factor to account for friction.

Best is to do it both ways to cross check your results.

 

[Don Bori]

Hi Baluncore, I appreciate the simplicity of your response, simple and yet informative. For the torque = Force x radius, why did you assume that the Force is 90deg-applied on the radius?

Welcome to PF.

With a stroke of 1000 mm the virtual crank will have a radius of 500 mm = 0.5m;
The area of the piston is Pi * (50mm)^2 = 7854 mm2 = 0.007854 m2;
2 Bar = 2 * 100 kPa = 200 kPa;
Piston force = 200 * 7.854 Newton = 1570.8 N;
Torque will be 0.5 m * 1570.8 N = 780 Nm.

Terminology confusion, see; https://en.wikipedia.org/wiki/Hydraulic_ram

 

[Baluncore]

For the torque = Force x radius, why did you assume that the Force is 90deg-applied on the radius?

Because torque is the force that is applied tangent to the circumference, multiplied by the radius r.

You have not specified the individual cylinder inlet and outlet valve type or timing so we cannot identify the crank angle at which maximum flow will occur.
If we assume you use ideal directional check valves on each cylinder inlet and outlet to common inlet and outlet manifolds, then;

If you use 4 cylinders separated by 90° then two cylinders will be generating 1/√2 = 0.7071 of their peak flow at the same time, so the total flow may be √2 of the individual cylinder peak flow. That would increase the torque I calculated by 1.4142
If on the other hand you save money by using only three cylinders, separated by 120° the peak flow will be as I calculated.

 

[Don Bori]

Baluncore, really appreciate your effort to accommodate my queries, but I still don't understand why my approach or how I understand it is different. I'm not an expert in Physics or Math so I really appreciate different inputs for my projects.

Scenario A: 4 cylinders, 90 deg. apart

Cylinder 1 (Clock Position 12) = 750mm distance between crankshaft center to the cylinder pin. Cylinder force is 180deg to the crankshaft so the Torque 1 is equal to 0.

Cylinder 2 (Clock Position 3) = approx. 500mm distance between crankshaft center to the cylinder pin, maximum force angle of the cylinder (from the alignment of crankshaft, pin, and cylinder), cylinder force is not tangent to the crankshaft so must consider Torque 3 = F x r x sin angle.

Cylinder 3 (Clock Position 6) = 250mm distance between crankshaft center to the cylinder pin. Cylinder force is 90deg to the crankshaft so the Torque 3 is equal to 0.

Cylinder 4 (Clock Position 9) = approx. 500mm distance between crankshaft center to the cylinder pin, maximum force angle of the cylinder (from the alignment of crankshaft, pin, and cylinder), cylinder force is not tangent to the crankshaft so must consider Torque 4 = F x r x sin angle.

Thank you Baluncore and to those who will contribute their knowledge or expertise in advance, your inputs will greatly contribute to the realization of my project.

 

[Baluncore]

Why would you build a 4 cylinder pump when an even numbers of cylinders produces more variation in flow than an odd number of cylinders? The magnitude of the ripple is greater with a 4 cylinder pump than with a 3 or 5 cylinder pump. 32% compared with 14% or 5% respectively.

Each cylinder will pump on one stroke or 180° of the full cycle. At the end of the induction stroke, when the piston is at BDC, the inlet valve will close and fluid will begin to be pushed through the outlet valve. The fluid will reach a maximum flow rate 90° later and then fall back to zero flow at 180° = TDC. That flow rate is proportional to the positive slope of a sinewave, which makes the flow a half cosine wave.

With more than n = two cylinders, the flow from a number of cylinders may be combined at one time. The total fluid pumped per revolution will be the number of cylinders, n, multiplied by the capacity of one cylinder. The average flow rate will be n / Pi.

n    Min flow   Peak flow  n / Pi    Ripple %
3     0.8660     1.0000    0.9549    14.0298
4     1.0000     1.4142    1.2732    32.5323
5     1.5388     1.6180    1.5915     4.9758
6     1.7321     2.0000    1.9099    14.0298
7     2.1906     2.2470    2.2282     2.5284
8     2.4142     2.6131    2.5465     7.8113
9     2.8356     2.8794    2.8648     1.5270
10     3.0777     3.2361    3.1831     4.9758
11     3.4776     3.5133    3.5014     1.0213

Notice that the fundamental frequency ripple is canceled for odd n, but not for even n.
Attached are some graphs showing flow rates and ripple for 3 to 7 cylinders.

3 cylinder

4 Cylinder

5 Cylinder

6 Cylinder

7 Cylinder

 

[Baluncore]

I believe you are being distracted by the slight variations in the angle of the cylinders. It is easier to start reasoning with the assumption that the cylinders remain at fixed phase angles.

If cylinder 2 is opposite cylinder 4, and both are pumping then you must be using the volume on both sides of the piston in both cylinders.
You have not yet specified the valve mechanism, nor have you shown the hydraulic connections to the cylinders, so it is still possible that you intend to use double acting cylinders that pump on both the extension and retraction stroke. If you do that you will have different cylinder capacity on either side of the piston due to the volume of the piston rod.

Your pump is similar to a radial aircraft engine. In that case the “big end” of the connecting rod was attached rigidly to one rod. That maintained the orientation of the big end as all other con-rods were pinned. It appears that radial engines always used an odd number of cylinders, usually 9.

I believe you should be considering 3 cylinders for your prototype. When that is working advance to 5 or 7 cylinders if there is an advantage in lower flow variation.

 

[anorlunda]

Temporarily closed for moderation.

 

[fresh_42]

Please respect our rules
https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/
They forbid any solicitation as well as a discussion on what looks like free energy.

Thread re-opened.

 

[jrmichler]

Expanding what @Baluncore said, a practical implementation of an N cylinder radial piston pump needs one master connecting rod with N-1 link connecting rods. Here is a good description of master and link rods: http://www.aviation-history.com/engines/radial.htm.

A photo I took two weeks ago showing a radial engine:

Good search terms for more info are radial engine master link rods. Radial engines fix the cylinders and use connecting rods with wrist pins, while your concept has the cylinders rocking back and forth. Either way can be made to work. With wrist pins, the cylinders need to be designed for the side forces. With rocking cylinders, the cylinders need to be designed for the sideways acceleration forces and the fluid connections will need either flexible hoses or swivel joints.

You have the option of building a prototype with one cylinder connected to the master rod, then adding more cylinders later. Doing it this way makes it faster and easier to work out details of bearings, seals, check valves, and fluid connections. Just machine the crankcase for as many cylinders as you want, then install one cylinder to start.

 

[Don Bori]

Thanks Jr, I bet that the feeling of seeing that kind of engine in actual is exhilarating!

Appreciate your technical tips especially the using of only 1 double-acting hydraulic cylinder as pump in the prototyping stage, any way the meaning of the prototyping is just to show the concept of how the idea will work.

As of now, I'm still in the idea stage and still in the basic calculations and still acquiring more advice from the experts.

Expanding what @Baluncore said, a practical implementation of an N cylinder radial piston pump needs one master connecting rod with N-1 link connecting rods. Here is a good description of master and link rods: http://www.aviation-history.com/engines/radial.htm.

A photo I took two weeks ago showing a radial engine:
View attachment 240788
Good search terms for more info are radial engine master link rods. Radial engines fix the cylinders and use connecting rods with wrist pins, while your concept has the cylinders rocking back and forth. Either way can be made to work. With wrist pins, the cylinders need to be designed for the side forces. With rocking cylinders, the cylinders need to be designed for the sideways acceleration forces and the fluid connections will need either flexible hoses or swivel joints.

You have the option of building a prototype with one cylinder connected to the master rod, then adding more cylinders later. Doing it this way makes it faster and easier to work out details of bearings, seals, check valves, and fluid connections. Just machine the crankcase for as many cylinders as you want, then install one cylinder to start.

 

[Don Bori]

I sincerely apologize for not observing the rules well, I missed to avoid the things which are prohibited for the benefit of this group.

Rest assured that I will be very careful in the following discussions.

Thank you very much for re-opening my thread.

Please respect our rules
https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/
They forbid any solicitation as well as a discussion on what looks like free energy.

Thread re-opened.

 

[Don Bori]

Hello! I'm planning to drive a 100W PMG generator motor by a hydraulic motor. Are my approach and calculations somehow correct? Thanks!